Energy Conversion and Management

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1 Energy Conversion and Management 51 21) Contents lists available at ScienceDirect Energy Conversion and Management journal homepage: Design and implementation of predictive current control of three-phase PWM rectifier using space-vector modulation SVM) Abdelouahab Bouafia a, *, Jean-Paul Gaubert b, Fateh Krim a a Laboratoire d Electronique de Puissance et Commande Industrielle LEPCI), Université de Sétif, Departement d électronique, Route de Bejaia, Setif, Algeria b Laboratoire d Automatique et d Informatique Industrielle LAII), ESIP, Université de Poitiers, France article info abstract Article history: Received 1 December 2 Received in revised form 2 September 29 Accepted 11 May 21 Available online 9 June 21 Keywords: PWM rectifiers Current control Predictive control Deadbeat control Space-vector modulation SVM) Unity power factor This paper is concerned with the design and implementation of current control of three-phase PWM rectifier based on predictive control strategy. The proposed predictive current control technique operates with constant switching frequency, using space-vector modulation SVM). The main goal of the designed current control scheme is to maintain the dc-bus voltage at the required level and to achieve the unity power factor UPF) operation of the converter. For this purpose, two predictive current control algorithms, in the sense of deadbeat control, are developed for direct controlling input current vector of the converter in the stationary a b and rotating d q reference frame, respectively. For both predictive current control algorithms, at the beginning of each switching period, the required rectifier average voltage vector allowing the cancellation of both tracking errors of current vector components at the end of the switching period, is computed and applied during a predefined switching period by means of SVM. The main advantages of the proposed predictive current control are that no need to use hysteresis comparators or PI controllers in current control loops, and constant switching frequency. Finally, the developed predictive current control algorithms were tested both in simulations and experimentally, and illustrative results are presented here. Results have proven excellent performance in steady and transient states, and verify the validity of the proposed predictive current control which is compared to other control strategies. Ó 21 Elsevier Ltd. All rights reserved. 1. Introduction The use of a three-phase PWM rectifier as a front-end stage represents an interesting solution for equipment which frequently works in regenerative operation, like adjustable speed drives ASDs) and distributed power generation system. This PWM ac dc converter offers several advanced features such as sinusoidal input currents at unity power factor, bidirectional power flow, small filter circuit, and high-quality dc output voltage. It is the new alternative technique for ac dc power conversion which draws a continuous sinusoidal current from the ac supply under all load conditions [1,2]. This dc-bus supply is essentially a PWM inverter with the normal ac output terminals connected to the ac line supply, and the usual dc input terminals become the common dc supply connection point. In fact, development of control methods for PWM rectifiers was possible thanks to advances in power semiconductor devices and digital signal processors, which allows fast operation * Corresponding author. addresses: bouafia_aou@yahoo.fr A. Bouafia), Jean.Paul.Gaubert@univpoitiers.fr J.-P. Gaubert), krim_f@ieee.org F. Krim). and cost reduction. It offers possibilities for implementation of sophisticated control algorithms in real-time. Various control strategies have been proposed in recent works on this type of PWM rectifier. They can be classified for their use of current loop controllers or active/reactive power controllers. The most commonly used control technique of indirect active and reactive power control is the two axis based method. Its principle resembles the field orientation used for vector-controlled ac motors. It is based on current vector orientation with respect to the voltage vector VOC) [3 ]. The unity power factor operation of the converter is achieved when the line current vector is aligned with the phase voltage vector of the power line supplying the PWM rectifier. VOC configuration uses two PI compensators of current vector components defined in rotating synchronous coordinate d q, this would result in tracking errors of controlled currents. Moreover, this control scheme requires coordinate transformation and decoupling between active and reactive components of input current. Therefore, implementation of control algorithm of VOC is complex and requires high sampling frequency to obtain satisfactory dynamic performance. To overcome this main drawback of VOC, we propose in this work to combine current control with predictive strategy using space-vector modulation /$ - see front matter Ó 21 Elsevier Ltd. All rights reserved. doi:1.116/j.enconman

2 2474 A. Bouafia et al. / Energy Conversion and Management 51 21) Over the last few years an interesting emerging control technique has been direct power control DPC) developed analogously with the well known direct torque control DTC) used for adjustable speed drives [9 16]. In DPC there are no internal current loops and the converter switching states are appropriately selected by a switching table, based on instantaneous errors between the commanded and estimated values of active and reactive power and the position of the power source voltage vector [9,1] or virtualflux vector position [11,12]. In this control scheme, the dc-bus voltage is regulated by adjusting the active power, and the unity power factor operation is achieved by controlling the reactive power to be zero. In Refs. [9,11,15], DPC configuration is based on a predefined switching table to select the converter switching states, using as input data variables tracking errors of active and reactive power and the position of the power source voltage vector or virtual-flux vector position. This switching table is considered optimal, although no further explanation is given about the generation of the table. The main drawbacks of this control scheme are the need for a high sampling frequency required to obtain satisfactory performance and the variable switching frequency. Both configurations of DPC proposed in [12,13] requires two PI controllers in active and reactive power control loops and need the estimation of virtual-flux vector. They have the advantage of constant switching frequency. However, the control algorithm is complex and requires high sampling frequency. Refs. [1,16] propose a configuration of DPC which is based of the calculation of an equivalent control vector allowing reduction of active and reactive power tracking errors and their first derivate. Finally, Ref. [14] presents a predictive DPC strategy where direct power control principle is combined with predictive selection of a voltage vectors sequence to satisfy minimisation criteria. This paper focuses on the predictive current control of threephase PWM rectifier with constant switching frequency. For this purpose, two digital predictive current control algorithms, in the sense of deadbeat control [17 2], are developed, allowing direct control of input current vector in both stationary a b reference frame and synchronous rotating d q reference frame. The basic idea of the current control scheme is to compute, at the beginning of each switching period, the rectifier average voltage vector which allows the cancellation of both tracking errors of input current vector components at the end of the switching period. Next, the spacevector modulation SVM) is employed to transform the computed average voltage vector on a sequence of switching states. The developed predictive current control algorithms were tested both in simulations and experimentally; using a dspace based experimental test bench. Illustrative results, showing the performance and the main advantages of the proposed current control strategy, are presented in this paper Predictive current control in a b reference frame The block diagram of the proposed predictive direct control of input current vector of three-phase PWM rectifier in the stationary a b reference frame is shown in Fig. 1. The symbols are defined as follows: e a, e b, e c three-phase power source voltages; v a, v b, v c ac terminal voltages of the PWM rectifier; i a, i b, i c three-phase line currents; S a, S b, S c switching states of the converter; L, r inductance and resistance of reactors; C, R L dc-link capacitor and load resistance. In this control scheme, the predictive current control algorithm is designed to compute the required rectifier average voltage vector, once every switching period, to be applied during the switching period T s, in order to null the tracking errors of current vector components, i a and i b, at the end of the switching period. As shown in Fig. 1, the power source voltage vector e ab, input current vector i ab, the dc-bus voltage controller output, and PLL output are used as input data variables of predictive current control algorithm. Referring to Fig. 1, the differential equations of the three-phase PWM rectifier can be expressed as follows: >< >: L dia e dt a r i a v a L di b e dt b r i b v b L dic e dt c r i c v c In the stationary reference frame a b and for a balanced threephase system, the line currents equation can be represented as: ð2þ dia 1 ðe dt L a v a r i a Þ di b 1 ðe dt L b v b r i b Þ The parameter r can be practically neglected and a discrete first order approximation of 2) can be adopted. So, line current vector components for the next sampling period are given by: i a ðk þ 1Þ i a ðkþþ Ts L ðe aðkþ v a ðkþþ i b ðk þ 1Þ i b ðkþþ Ts L ðe bðkþ v b ðkþþ ð1þ ð3þ 2. Predictive current control principle Current control CC) of PWM converters is one of the most important subjects of modern power electronics. The main task of the control scheme in CC PWM converter is to force the controlled currents to follow the reference signals. Existing current control techniques can be classified as linear and nonlinear controllers. Linear controllers operate with conventional voltage-type PWM modulators in which current error compensation and voltage modulation are clearly separated. The nonlinear current control group includes hysteresis, delta modulation, and on-line optimized controllers [2]. In this section, two current control algorithms based on predictive control strategy are designed to achieve unity power factor UPF) operation of the three-phase PWM rectifier, with fixed switching frequency using space-vector modulation SVM). Fig. 1. Block diagram of predictive current control for three-phase PWM rectifier in a b reference frame.

3 A. Bouafia et al. / Energy Conversion and Management 51 21) If the sampling period, T s, is assumed to be small in comparison with the period of the power source voltages, the components e a and e b are assumed constant over the period T s. On the other hand, rectifier voltage vectors applied during T s are represented by their equivalent average voltage vector [v a k) v b k)] T. The objective of the control system is to make the input current vector at the next sampling instant equal to the desired reference value by forcing: i a ðk þ 1Þ i aðk þ 1Þ i b ðk þ 1Þ i bðk þ 1Þ By replacing 4) in 3), the required rectifier average voltage vector to be generated during the switching period, T s, is obtained by solving the resulting Eq. 3): v a ðkþ e a ðkþ L T s i L aðk þ 1ÞþT s i a ðkþ v b ðkþ e b ðkþ L T s i L bðk þ 1ÞþT s i b ðkþ As shown in Fig. 1, the dc-bus voltage is regulated by adjusting input current magnitude, I max, delivered from the outer proportional-integral dc-bus voltage controller. It can be assumed constant over the switching period T s because T s is very small compared to time-constant of PI controller). Therefore, the predicted value of input current vector at the next sampling instant can be estimated with two methods: Without PLL block In this case, current vector is considered proportional to the power source voltage vector as follows: i ab ðk þ 1Þ G e abðk þ 1Þ For a balanced purely sinusoidal supply, the power source voltage vector at the next sampling instant can be derived from e a and e b components at the current time through rotation of the angle xt s as the following: e a ðk þ 1Þ e b ðk þ 1Þ cosðxt sþ sinðxt s Þ sinðxt s Þ cosðxt s Þ e a ðkþ e b ðkþ ð4þ ð5þ ð6þ ð7þ commands of input current vector components, i q set to zero for UPF) and i d delivered from the outer proportional-integral dcbus voltage controller), input current vector i dq, and power source voltage vector e dq, are used as input data variables of the predictive current control algorithm block. In the rotating d q reference frame and for a balanced threephase system, the line currents equation can be represented as [4,5]: di d 1 ðe dt L d v d þ x L i q Þ ð11þ di q 1 ðe d L q v q x L i d Þ In order to decouple the two differential equations, assuming that: ð12þ v d u d þ x L i q v q u q x L i d By means of a discrete first order approximation of 11), input current vector components, i d and i q, for the next sampling period are obtained as follows: i d ðk þ 1Þ i d ðkþþ Ts L ðe dðkþ u d ðkþþ i q ðk þ 1Þ i q ðkþþ Ts L ðe qðkþ u q ðkþþ i d * k+1) i d * k-1) Fig. 2. Predicted value estimation of i d command. T s T s ð13þ Thus, the required rectifier average voltage vector is given by the following expression: v a ðkþ e aðkþ L G cosðxt s Þ sinðxt s Þ e a ðkþ v b ðkþ e b ðkþ T s sinðxt s Þ cosðxt s Þ e b ðkþ þ L i a ðkþ ðþ T s i b ðkþ With PLL block In this case, the predicted value of input current vector is obtained as follows: qffiffi < i 3 aðk þ 1Þ I 2 max sinðh þ xt s Þ qffiffi ð9þ : 3 ðk þ 1Þ I max cosðh þ xt s Þ i b v a ðkþ v b ðkþ 2 By replacing 9) in 5), the rectifier average voltage vector is given by the following equation: e rffiffiffi aðkþ 3 L:Imax sinðh þ xt s Þ þ L i a ðkþ e b ðkþ 2 T s cosðh þ xt s Þ T s i b ðkþ 2.2. Predictive current control in d q reference frame ð1þ Fig. 3 shows the configuration of the proposed predictive current control in rotating d q reference frame. In this scheme, Fig. 3. Block diagram of predictive current control for three-phase PWM rectifier in d q reference frame. Table 1 Electrical parameters of power circuit. Sampling frequency, T s Resistance of reactors, r Inductance of reactors, L dc-bus capacitor, C Load resistance, R L Line to line ac voltage peak value Power source voltage frequency, f dc-bus voltage, v dc 15 khz.56 X 19.5 mh 11 lf 6 X 12 V 5 Hz 1 V

4 2476 A. Bouafia et al. / Energy Conversion and Management 51 21) To make the input current vector at the next sampling instant equal to the desired reference value, we impose the following equalities: i d ðk þ 1Þ i dðk þ 1Þ i q ðk þ 1Þ i qðk þ 1Þ ð14þ As shown in Fig. 3, the command i q is constant, equal to zero for unity power factor operation, and given from the exterior. So, we can assume that: i q ðk þ 1Þ i q ðkþ ð15þ However, the command i d is provided by the outer proportionalintegral dc-bus voltage controller. If tracking error of dc-bus voltage is assumed constant over two successive sampling periods, the predicted value of i d, at the next sampling instant k + 1), can be estimated using a linear extrapolation as shown in Fig. 2. The reference value of this current at the next sampling instant can be estimated using the following relation: i d ðk þ 1Þ 2 i d ðkþ i dðk 1Þ ð16þ 12 v α v β 4-4 i β i α e a i a i b i c v dc Mag % of Fundamental) 1 5 Harmonic order Fig. 4. Simulation results in steady state for predictive current control in a b reference frame from the top: computed v a /1 and v b /1, i a and i b ; e a, i a, i b and i c ; dc-bus voltage; input current spectrum.

5 A. Bouafia et al. / Energy Conversion and Management 51 21) By replacing 15) and 16) in 13) we obtain the predictive current control law: u d ðkþ u q ðkþ e dðkþ e q ðkþ L T s " e id ðkþþdi d ðkþ # e iq ðkþ ð17þ where e id k) and e iq k) are the actual tracking errors of input current components i d and i q, respectively, and Di d k) is the actual change in i d command. By replacing 17) in 12), the required rectifier average voltage vector allowing cancellation of tracking errors of both input current vector components, at the end of the switching period, is given by the following expression: e " dðkþ L e id ðkþþdi d ðkþ # þ x L i qðkþ ð1þ e q ðkþ T s e iq ðkþ x L i d ðkþ v d ðkþ v q ðkþ To use the SVM, transformation from rotating d q coordinates to static a b coordinates is necessary by using the following matrix transformation: v a ðkþ v b ðkþ sinðhþ cosðhþ v d ðkþ cosðhþ sinðhþ v q ðkþ ð19þ 12 v d 4 i d i q -4 - v q e a i a i b i c v dc Mag % of Fundamental) 1 5 Harmonic order Fig. 5. Simulation results in steady state for predictive current control in d q reference frame from the top: computed v d /1 and v q /1, i d and i q ; e a, i a, i b and i c ; dc-bus voltage; input current spectrum.

6 247 A. Bouafia et al. / Energy Conversion and Management 51 21) currents have nearly sinusoidal waveforms THD =.614%) and in phase with their corresponding power source voltages, thus guaranteeing operation with a power factor very close to one. The dc-bus voltage is very close to its reference value. For the second predictive current control algorithm, Fig. 5 shows that the controlled current vector components, i d and i q, by applying the computed components of the rectifier average voltage vector v d and v q, are constant and very close to their reference values, where i q is equal to zero in average. The input currents have nearly sinusoidal waveforms THD =.634%) and in phase with their corresponding power source voltages, thus guaranteeing operation with unity power factor. Also, the dc-bus voltage is very close to its reference value. Fig. 6. Different parts of experimental test bench and its control system: 1 PWM rectifier, 2 dspace I/O connectors, 3 isolating transformer, 4 interconnecting reactance, 5 HZ64, 6 PR3). 3. Simulation results Both predictive current control algorithms, Eqs. 1) and 1), developed in this work have been simulated using Matlab/Simulink MT tool. The main electrical and control parameters, used in simulation and implementation tests, are shown in Table 1. The following simulation results are obtained for purely sinusoidal power source voltages. For the first predictive current control algorithm, Fig. 4 shows that the input current vector components, i a and i b, controlled by applying the computed control vector v a and v b, are very close to sinusoidal waveforms and are in quadrature. As a result, input 4. Experimental system and results The developed predictive current control algorithms have been tested at a three-phase PWM rectifier. The specifications of the experimental system are as shown previously in Table 1. The test bench, shown in Fig. 6, has been developed in LAII-laboratory France. It consists of a three-phase IGBT based inverter of 2 kva SEMIKRON) with anti-paralleling diodes module SKM 4 GB 121D) and three 2 two-channel driver SKHI 21), which plays the role of PWM rectifier. Two Hall-effect CT s LEM PR3) and three isolation amplifiers HAMEG HZ64) are used to measure two input currents i a and i c ), the dc-bus voltage and two line to line power source voltages, e ab and e ca, respectively. The predictive current control algorithms run under the Matlab/ Simulink MT environment in a dspace DSP system DS114) realtime platform inserted in a PC-Pentium. Slave DSP three-phase PWM generation block is used to convert duty cycles provided by Fig. 7. Experimental waveforms in steady state for predictive current control in a b reference frame for v dc = 1 V. Fig.. experimental measurements for predictive current control in a b reference frame for v dc = 1: THD of i a and THD of e a ; b) input currents and power source voltages phasors.

7 A. Bouafia et al. / Energy Conversion and Management 51 21) space-vector modulation to PWM signals S a, S b and S c. The different coordinate transformations used in this work are showed in the Appendix A. The corresponding experimental results in steady state, for the developed predictive current control algorithms, in a b and d q reference frame, are presented in Figs. 7 and and Fig. 9, respectively. From these figures, it can be seen that experimental results are very close to the previous simulation results; this proves the validity of the proposed predictive current control. In both predictive current control algorithms the dc-bus voltage tracks its reference with a good accuracy and stability. For the first current control algorithm, the controlled currents, i a and i b, are very close to their references and have nearly sinusoidal waveforms. Therefore, input currents are very close to sin wave and in phase with line power source voltages. Unity power factor operation of the converter is successfully achieved as indicate experimental measurements as shown in Fig. THD = 1.9%, u =1, PF =.993). For the second predictive current control algorithm, controlled currents, i d and i q, track their references with good accuracy and stability. Also, i q is maintained very close to zero, this makes input currents waveforms nearly sinusoidal and the power factor close to one THD = 2%, u =1, PF =.993) as shown in Fig. 9. In order to compare the proposed predictive current control performance to other control strategies, Fig. 1 and Fig. 11 show experimental results obtained by applying hysteresis current control HCC) method and switching table based direct power control DPC) technique to three-phase PWM rectifier, respectively. For the same circuit parameters, shown previously in Table 1, results of the proposed predictive current control are close to those of hysteresis current control method. However, the proposed current control operates with constant switching frequency and HCC operates with variables switching frequency. Also, the proposed control is much better than DPC using the switching table presented in [9]. It can be seen from Fig. 11 that input currents for DPC are distorted because the used switching table is not optimal and instantaneous active and reactive powers are poorly controlled. Simulation results of both control strategies HCC and DPC) are very close to the experimental results presented in this work. Fig. 12 shows experimental results of response during a double change in the load power increasing of 5% and decreasing of 33.33%). It is noticeable that for this test, there is smooth control of controlled currents, i a, i b ) and i d,i q ), and smooth control of the dc-bus voltage which decreases from the reference value, in case of step on, to deliver the energy during the transient period, Fig. 1. Experimental waveforms in steady state for hysteresis current control for v dc = 1 V. Fig. 11. Experimental waveforms in steady state for DPC using switching table for v dc = 1 V. and increases in case of step down. Also, it can be observed that for both predictive current control algorithms the unity power Fig. 9. Experimental waveforms in steady state for predictive current control in d q reference frame for v dc = 1 V.

8 24 A. Bouafia et al. / Energy Conversion and Management 51 21) Fig. 12. Step on/down of the load power for the proposed predictive current control in: a) a b reference frame; b) d q reference frame. Experimental results show that the proposed control is better than direct power control DPC) using switching table and hysteresis current control strategies. Appendix A For a balanced three-phase system defined as follows: e a ðhþ A sinðhþ; e b ðhþ A sinðh 2p=3Þ; e c ðhþ A sinðh 4p=3Þ Fig. 13. Transient of the step change of v dc, for predictive current control in a b reference frame, decreasing from 22 to 1 V. factor operation of the converter is successfully maintained, even in this transient state. The dynamic behavior of the proposed predictive current control algorithm, in a b reference frame, under a step change of v dc, in case of decreasing, is presented in Fig. 13. After a short transient, the dc-bus voltage is maintained close to its new reference with good accuracy and stability. The controlled current vector components, i a and i b, are very close to their references and the obtained input currents have nearly sinusoidal waveforms. 5. Conclusion This paper has presented the design and implementation of predictive current control of three-phase PWM rectifier with constant switching frequency, using space-vector modulation SVM). Two predictive current control algorithms were developed, allowing direct control of input current vector components in the stationary a b and rotating d q reference frame, respectively. Simulation and experimental results have proven excellent performance of the proposed current control, even in transient and steady states. Precise regulation and good stability of the dc-bus voltage, nearly sinusoidal waveform of input currents and power factor close to one are successfully achieved with both control algorithms tracking error of v dc 6 1 V, input current THD 6 2%). Simulation and The different transformations are obtained as follows: 2 3 rffiffiffi x a x a 2 1 1=2 1=2 p ffiffiffi p ffiffiffi x b 5 x b 3 3 =2 3 =2 x c x d sinðhþ cosðhþ xa cosðhþ sinðhþ x q x d x q x b 2 3 rffiffiffi x a 2 sinðhþ sinðh 2p=3Þ sinðh 4p= x b 5 3 cosðhþ cosðh 2p=3Þ cosðh 4p=3 rffiffiffi 1 e a ðe ab e ca Þ; 6 References rffiffiffi 1 e b ðe ab þ e ca Þ 2 [1] Singh B, Singh BN, Chandra A, Al-haddad K, et al. A review of three-phase improved power quality AC DC converters. IEEE Trans Ind Electron 24;513): [2] Rodriguez JR, Dixon JW, Espinoza JR, Pontt J, Lezana P. PWM regenerative rectifiers: state of the art. IEEE Trans Ind Electron 25;521):5 22. [3] Kazmierkowski MP, Malesani L. Current control techniques for three-phase voltage source PWM converter: a survey. IEEE Trans Ind Electron 199;455): [4] Kwon BH, Youm JH, Lim JW. A line voltage-sensorless synchronous rectifier. IEEE Trans Power Electron 1999;145): [5] Liserre M, Dell Aquila A, Baabjeerg F. Genetic algorithm-based design of the active damping for an LCL-filter three-phase active rectifier. IEEE Trans Power Electron 24;191):76 6. [6] Malinowski M, Kazmierkowski MP, Trzynadlowski A. Review and comparative study of control techniques for three-phase PWM rectifiers. Math Comput Simul 23;63: [7] Malinowski M, Bernet S. A simple voltage sensorless active damping scheme for three-phase PWM converters with LCL filter. IEEE Trans Ind Electron 2;554):171. [] Yin B, Oruganti R, Panda SK, Bhat AKS. An output power control strategy for a three-phase PWM rectifier under unbalanced supply conditions. IEEE Trans Ind Electron 2;555): [9] Noguchi T, Tomiki H, Kondo S, Takahashi I. Direct power control of PWM converter without power source voltage sensors. IEEE Trans Ind Appl 199;343): x c

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